LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)
The continuation of text review:
Key symbols
≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0 = Null class
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Classes as 'primitive concepts' in a system
Philosopher Langer expresses the idea that there are clear and economical propositions that express the entire system with a few symbols. (166). This rests on a tedious process of translation and re-translation. (166).
Most that have been following this review, which is alternated with other articles, will likely agree that learning symbol logic is indeed tedious!
It has been billed by Langer as (paraphrased) an academic alternative to more confusing syntax language, but in reality, in my humble opinion, only a few academic types in philosophy and mathematics will find learning symbolic logic helpful.
Even so, as my PhD (Wales) was in Theology and Philosophy of Religion, it is useful to learn more symbolic logic than the little amount I did during writing my British theses. At the same time, there are some good lessons to learn in regard to logic and reason from Philosopher, Langer.
Langer states that classes are not empty. They are not zero. (166). A class in not 0 = null class.
(∃! wt) : ˜ (0)
There exists white houses equals not null class. White houses are a class.
Symbolic logic requires a formal context in order for anything to be stated. (166-167). A great difficulty is that the typical reader will not grasp the context of symbolic logic, and/or especially in a 2017, Western context, which is in general, distinctly non-philosophical, even have the desire to attempt to learn the context of any symbolic logic.
Primitive concepts, terms and relations, within symbolic logic are not explained, but are simply 'taken for granted'. (167). These meanings are provided by interpretation only in the context provided. (167). The symbols for houses and related is an example as these symbolic interpretations. (167).
The author writes that to avoid ambiguity with literary grammar and syntax. words are replaced in symbolic logic with arbitrary symbols. (52).
Having reviewed now nearly half of this textbook, I can grant that technically, Langer's premise could be correct, I suppose. Symbolic logic could be more clear than literary, grammar and syntax.
However, practically, even most academics are more familiar with syntax language than symbolic logic, and it is an understatement to write that this will not change any time soon.
